Existence of r-fold perfect (v,K,1)-Mendelsohn designs with K⊆{4,5,6,7}

AbstractLet v be a positive integer and let K be a set of positive integers. A (v,K,1)-Mendelsohn design, which we denote briefly by (v,K,1)-MD, is a pair (X,B) where X is a v-set (of points) and B is a collection of cyclically ordered subsets of X (called blocks) with sizes in the set K such that every ordered pair of points of X are consecutive in exactly one block of B. If for all t=1,2,…,r, every ordered pair of points of X are t-apart in exactly one block of B, then the (v,K,1)-MD is called an r-fold perfect design and denoted briefly by an r-fold perfect (v,K,1)-MD. If K={k} and r=k−1, then an r-fold perfect (v,{k},1)-MD is essentially the more familiar (v,k,1)-perfect Mendelsohn design, which is briefly denoted by (v,k,1)-PMD. In this paper, we investigate the existence of r-fold perfect (v,K,1)-Mendelsohn designs for a specified set K which is a subset of {4, 5, 6, 7} containing precisely two elements

FLORIDA\u27S DOWNTOWNS: THE KEY TO SMART GROWTH, URBAN REVITALIZATION, AND GREEN SPACE PRESERVATION

This article reviews Florida\u27s growth management system, which has spurred suburban development, and its negative impact on Florida\u27s cities. As Florida\u27s governor and legislature have turned their focus to this issue, this article evaluates policy recommendations to limit Florida\u27s suburban sprawl and invigorate its urban centers

Linear spaces with many small lines

AbstractIn this paper some of the work in linear spaces in which most of the lines have few points is surveyed. This includes existence results, blocking sets and embeddings. Also, it is shown that any linear space of order v can be embedded in a linear space of order about 13v in which there are no lines of size 2

Addressing the Nation: The Use of Design Competitions in Interpreting Historic Sites

Design competitions are regularly used for the creation of monuments and structures in the United States. Pursuing this method to develop the interpretation of a historic site or monument, encompassing more than the design of the site and its structures, however, is a rarer and more recent phenomenon. This thesis evaluates the use of design competitions in the design and interpretation of historic sites that could be considered recent sites of conscience. This type of site is especially difficult to interpret, given its sometimes controversial status. The interpretation and design of a historic site significantly impacts a visitor’s perception of an event, a people, or the history of a location. It is responsible for creating what the visitor takes with them. A process this important must be carefully pursued and evaluated, especially when the content requires the designer to address the nation. The sites evaluated in this thesis (Women\u27s Rights National Historical Site, Little Bighorn Battlefield National Monument, and Flight 93 National Memorial) represent different stages of the process, ranging from a site that opened in 1980 (Women\u27s Rights) to a site currently undergoing the construction of its chosen design (Flight 93). These design competitions, in response to a call for interpretation of a historic site marred by national and regional trauma or upheaval, reveal the lessons learned from the event and stimulate the next steps to occur on the site. They additionally allow opportunities for a variety of viewpoints to be expressed and considered in a juried atmosphere

Phase retrieval for characteristic functions of convex bodies and reconstruction from covariograms

We propose strongly consistent algorithms for reconstructing the characteristic function 1_K of an unknown convex body K in R^n from possibly noisy measurements of the modulus of its Fourier transform \hat{1_K}. This represents a complete theoretical solution to the Phase Retrieval Problem for characteristic functions of convex bodies. The approach is via the closely related problem of reconstructing K from noisy measurements of its covariogram, the function giving the volume of the intersection of K with its translates. In the many known situations in which the covariogram determines a convex body, up to reflection in the origin and when the position of the body is fixed, our algorithms use O(k^n) noisy covariogram measurements to construct a convex polytope P_k that approximates K or its reflection -K in the origin. (By recent uniqueness results, this applies to all planar convex bodies, all three-dimensional convex polytopes, and all symmetric and most (in the sense of Baire category) arbitrary convex bodies in all dimensions.) Two methods are provided, and both are shown to be strongly consistent, in the sense that, almost surely, the minimum of the Hausdorff distance between P_k and K or -K tends to zero as k tends to infinity.Comment: Version accepted on the Journal of the American Mathematical Society. With respect to version 1 the noise model has been greatly extended and an appendix has been added, with a discussion of rates of convergence and implementation issues. 56 pages, 4 figure